Backward Induction
Backward induction involves working backward from maturity to time 0 to determine a bond’s value at each node. It makes the following assumptions: The value of a bond is known at maturity (Final coupon payment + Face value). The value…
Binomial Interest Rate Model
Modeled future interest rates can take on different possible values, depending on the level of volatility assumed. This can be shown using an interest rate tree framework. One of the most popular tools used is the binomial interest rate model….
Arbitrage Free Value
Bonds can be valued either using the traditional valuation approach or the arbitrage-free valuation approach. Under the traditional valuation approach, a single interest rate is used to discount all of a bond’s cash flows. In this approach, all cash flows of…
Arbitrage-Free Valuation of a Fixed Income Security
Arbitrage free valuation is an approach that determines bond values based on the assumption that arbitrage opportunities do not exist. The arbitrage-free valuation model is based on the law of one price, which states that two goods, which are perfect…
Maturity Structure of Yield Volatilities
Bond managers must quantify interest rate volatilities for bonds with embedded options because their values depend on the level of interest rate volatilities. Additionally, mitigating the effect of interest rate volatilities on a bond’s price volatility is part of risk…
Measuring Bond Exposure
Shaping risk is the sensitivity of a bond’s price to changes in the shape of the yield curve. An active bond investor trades based on the predicted shape of the yield curve. Yield curve risk is the bond portfolio exposure…
Developing Interest Rate Views Using Macroeconomic Variables
Key economic factors and market events influence interest rate dynamics such as the curvature, level, and steepness of the yield curve and changes in spot versus forward rates. Fixed-income traders use implied forward rates as market-neutral reference points. Active fixed…
Traditional Theories of the Term Structure of Interest Rates
The term structure is a relationship between interest rates and maturities of similar quality bonds. A yield curve is a graphical representation of the term structure of interest rates. The following theories explain the term structure of interest rates and…
Short Term Interest Rate Spreads
Market participants often use short-term interest rate spreads to evaluate liquidity and credit risk. A good example is the TED spread, which is a key indicator of perceived liquidity and credit risk. TED is formed from an abbreviation US T-bill…
Swap Spread
The swap spread is obtained by taking the difference between a swap’s fixed leg rate and the yield on a recently issued government bond (“on the run issue”) with the same maturity. Swap spreads can be used to value bonds….
